Journal of Experimental Psychology:
Human Perception and Performance
2002, Vol. 28, No. 5, 1202–1212
Copyright 2002 by the American Psychological Association, Inc.
0096-1523/02/$5.00 DOI: 10.1037//0096-1523.28.5.1202
Dissociation Between Location and Shape in Visual Space
Jack M. Loomis
John W. Philbeck
University of California, Santa Barbara
George Washington University
Pavel Zahorik
University of Wisconsin—Madison
There are often large perceptual distortions of shapes lying on the ground plane, even in well-lit
environments. These distortions occur under conditions for which the perception of location is accurate.
Four hypotheses are considered for reconciling these seemingly paradoxical results, after which 2
experiments are reported that lend further support to 1 of them—that perception of shape and perception
of location are sometimes dissociable. The 2 experiments show that whereas perception of location does
not depend on whether viewing is monocular or binocular (when other distance cues are abundant),
perception of shape becomes more veridical when viewing is binocular. This means that perception of
shape is not fully constrained by the perceived locations of the vertices that define the shape.
adjoining depth extent (in the median sagittal plane). In one such
experiment (Loomis, Da Silva, Fujita, & Fukusima, 1992), observers adjusted depth extents defined by targets on the ground to be
physically equal to width extents, also defined by targets on the
ground. Even under these objective instructions, depth extents
positioned from 3 to 12 m away had to be made 1.5 to 1.9 times
as large as the width extents to be judged as equal. In a related
experiment, Beusmans (1998) obtained evidence of even greater
distortion, again using objective instructions. In his experiment,
observers adjusted the width extents to match the depth extents.
For small extents positioned more than 15 m away, observers
judged width extents to be equal to depth extents that were 2.5 to
5 times larger!
Other evidence of systematic perceptual distortion of shape has
been obtained with slightly different procedures and stimuli (Baird
& Biersdorf, 1967; Levin & Haber, 1993; Loomis & Philbeck,
1999; Norman, Todd, Perotti, & Tittle, 1996; Philbeck, 2000;
Ribeiro, Fukusima, & Da Silva, 1995; Tittle, Todd, Perotti, &
Norman, 1995; Todd, Tittle, & Norman, 1995; Toye, 1986; Wagner, 1985). Perceptual distortions of related origin have also been
reported in connection with the judgment of the slants of hills
(Bhalla & Proffitt, 1999; Proffitt, Bhalla, Gossweiler, & Midgett,
1995) and of the angles of corners of buildings (Hecht, van Doorn,
& Koenderink, 1999). Moreover, Beusmans (1998) conducted a
second experiment that involved the matching of two depth extents
within the median sagittal plane, one more distant than the other.
Striking failures of shape constancy are commonplace in natural
environments viewed under full cues. As an example, Figure 1
shows two views of a portion of a popular walkway in Barcelona,
Spain. The gray and white tiles define a sinusoidal profile of
constant modulation depth (in the direction of the walkway) and
constant wavelength (in the orthogonal direction). Conflicting
sharply with the constant physical depth modulation is the strong
impression of a decreasing modulation with distance that disappears within just a few meters; this impression holds whether one
is viewing the figure or binocularly viewing the walkway in
person. The variation in apparent depth modulation (upper panel)
is a striking failure of shape constancy in the presence of abundant
distance cues. In a similar manner, when one looks sideways at the
walkway (bottom panel), the undulation appears to exaggerate
with increasing distance, another striking failure of shape
constancy.1
A number of experiments have confirmed that failures of shape
constancy in the natural world are robust and commonplace. In
many of these experiments, perceived shape is assessed by having
observers match a width extent (in a frontoparallel plane) to an
Jack M. Loomis, Department of Psychology, University of California,
Santa Barbara; John W. Philbeck, Department of Psychology, George
Washington University; Pavel Zahorik, Waisman Center, University of
Wisconsin—Madison.
This research was supported by Office of Naval Research Grant
N00014-95-1-0573 and National Science Foundation Grant DBS 8919383.
Preliminary reports of Experiments 1 and 2 were presented at the annual
meetings of the Psychonomic Society in November 1994 (St. Louis,
Missouri) and November 1999 (Los Angeles, California), respectively. We
thank Nicole Lorenzo and Christopher Blaylock for assistance with the
experiments, and John Foley and two anonymous reviewers for comments
on earlier versions of the article.
Correspondence concerning this article should be addressed to Jack M.
Loomis, Department of Psychology, University of California, Santa Barbara, California 93106-9660. E-mail: loomis@psych.ucsb.edu
1
Shape constancy refers to the invariance of perceived shape under a
variety of viewing conditions, many of which cause a change in the retinal
projection of the distal shape. Constancy and veridicality (accuracy) of
shape perception are not the same, in that it is possible for the perception
of shape to be nonveridical over viewing conditions and yet exhibit
constancy. Although we recognize this, when we refer to failures of shape
constancy, we wish it to be understood that there is generally nonveridicality of shape perception as well.
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DISSOCIATION OF LOCATION AND SHAPE
Figure 1. Two views of Las Ramblas walkway in Barcelona, Spain. The
gray and white tiles define sinusoidal stripes that extend from one edge of
the walkway to the other and that are uniform in modulation depth along
the length of the walkway. Contrasting with the uniform stimulus, visual
perception exhibits a dramatic failure of shape constancy, even when one
views the walkway binocularly under good lighting conditions. That is,
when one looks down the length of the walkway, the depth modulation
appears to decrease with distance, as is apparent in the top panel. Conversely, when one looks to the side, the curvature of the sinusoidal
modulation appears to increase with distance, as is apparent in the bottom
panel.
Here too evidence of large perceptual distortion was obtained, with
the farther extent having to be nearly twice as large as the nearer
one for them to be judged as equal. All of these experiments
indicate large distortions of shape and relative extent under fullcue viewing.
These failures of shape constancy under full-cue viewing are not
unexpected when one considers the enormous challenge that the
visual system must confront when processing shapes that vary
greatly in perspective. For example, a little-appreciated fact, even
among vision researchers, is the degree of anisotropy in the perspective of patterns viewed at a slant (see Gillam, 1981). As a
square pattern moves along the ground away from a viewing point,
its angular width is approximately inversely proportional to its
1203
distance; meanwhile, its angular height (corresponding to depth in
the ground plane) is approximately inversely proportional to the
square of its distance (Gillam, 1981; Purdy, 1960). The ratio of
angular height to angular width is equal to the cosine of the optical
slant, which is the angle between the normal to a surface patch and
the line of sight to that patch (Gibson & Cornsweet, 1952; Joynson
& Newson, 1962; Kaiser, 1967; Purdy, 1960; Sedgwick, 1983;
Wallach & Moore, 1962); for a person of average height, the
aspect ratio of a small square texture element 10 m away is only
0.17.
Despite the large changes in perspective of a target as it varies
in distance, there is by no means a complete absence of shape
constancy. Humans are able to compensate partially for the retinal
perspective and consequently perceive shapes closer to the distal
(e.g., Beck & Gibson, 1955; Joynson & Newson, 1962; Pizlo,
1994; Pizlo & Stevenson, 1999; Sedgwick, 1986; Thouless, 1931).
Loomis and Philbeck (1999) found that judgments of the aspect
ratios of L-shaped objects on the surface plane were roughly
midway between the distal and retinal values.
Loomis and Philbeck (1999) also found that the degree of
perceptual distortion increased slightly with egocentric distance of
the L-shaped objects, a result apparent as well in the extent
matching studies of Beusmans (1998) and Loomis et al. (1992). At
first glance, it might appear that the increasing perceptual shape
distortion with distance is the consequence of diminishing effectiveness of distance cues, such as accommodation, convergence,
and binocular disparity. However, by using projectively equivalent
L-shaped figures at two scales differing by a factor of three,
Loomis and Philbeck (1999) found that the degree of distortion
was independent of scale for monocular viewing and nearly so for
binocular viewing; their finding suggests that the perceptual shape
distortion is much more dependent on the optical slant of the 2-D
pattern being judged than on its egocentric distance, whether
physical or perceived.
Given the just-mentioned misperceptions of shape and extent,
one might expect that perception of egocentric distance under the
same conditions would also exhibit substantial error, possibly in
the form of a compressive nonlinearity between physical and
perceived distance (e.g., Gilinsky, 1951). Yet, a number of recent
studies involving visually directed action, such as blind walking
toward a previewed target, have demonstrated that perception of
egocentric distance under similar conditions is both linear in
physical distance and accurate out to at least 20 m (Elliott, 1986,
1987; Fukusima, Loomis, & Da Silva, 1997; Loomis et al., 1992;
Loomis, Klatzky, Philbeck, & Golledge, 1998; Philbeck & Loomis, 1997; Philbeck, Loomis & Beall, 1997; Rieser, Ashmead,
Talor, & Youngquist, 1990; Sinai, Ooi, & He, 1998; Steenhuis &
Goodale, 1988; Thomson, 1983; for a summary, see Loomis &
Knapp, in press). The accuracy with which egocentric distance is
perceived appears to conflict with the systematic misperception of
shape and extent under similar conditions.
Four Hypotheses
Loomis et al. (1992) and Philbeck (2000) presented three hypotheses that might potentially reconcile the accurate egocentric
responding with the systematic distortion of shape and of perceived extents. Here we add a fourth. The four hypotheses need not
be exclusive.
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LOOMIS, PHILBECK, AND ZAHORIK
Before presenting the hypotheses, we define some terms. Egocentric distance is the distance between a target location and the
observer. Strictly speaking, egocentric distance is measured only
along a radial direction from the observer (a line of sight), but
occasionally we use it to refer to distance along a horizontal plane
(e.g., the ground) in cases in which the primary variation is in a
radial direction. Perceived egocentric distance is the corresponding perceived distance. Perceived location refers to the perceived
egocentric distance of a target and its perceived direction, which is
generally considered to be accurate (for clear evidence, see Ooi,
Wu, & He, 2001). Exocentric distance is the distance (extent)
between two target locations, neither of which coincides with the
observer. (In the vision literature, exocentric distance often has
meant the separation between two locations in a radial direction,
but we do not so restrict the meaning here.) Perceived exocentric
distance is the perceived extent between two locations.
Perceived shape of a 2-D figure in 3-D space is assumed to be
determined by the perceived exocentric distances between its various vertices; for example, the perceived shape of a rectangle lying
on the ground and oriented toward the observer is determined by
the ratio of its perceived width (in a frontoparallel plane) and its
perceived depth (in the median sagittal plane). A depth extent,
strictly speaking, is an exocentric distance lying in a radial direction. In the preceding presentation of the empirical findings, what
were referred to as depth extents (those lying in both the ground
plane and the median sagittal plane) were not depth extents in the
strict sense, because they did not lie along lines of sight; still, most
of their variation was in a radial direction. For ease of exposition,
here we continue to use the less strict meaning. The definition of
width extent is even more problematic, because points along any
straight line necessarily vary in distance from the observer. However, line segments that subtend only a few degrees and are both
symmetric about and perpendicular to a line of sight are prototypical of what we mean by width extents.
Hypothesis 1: Accurate Perception of Location and
Dissociation of Location and Shape
This hypothesis, first put forth by Loomis et al. (1992) and later
elaborated by Loomis, Da Silva, Philbeck, and Fukusima (1996),
assumes that location is perceived accurately (i.e., without systematic error) out to at least 20 m under full-cue conditions. Because
perceived shapes under the same conditions are perceived with
large systematic error, the hypothesis further assumes that perceptions of extent and of shape are based on neural computations
different from those involved in perception of location. In particular, it assumes that perceptions of extent and of shape are not fully
constrained by the perceived locations of the vertices defining the
extent or shape (see also Baird & Biersdorf, 1967). This means that
perceptions of extent or shape can vary even when the perceived
locations of the vertices defining the extent or shape remain
constant. Strong support for this idea in the context of reaching and
grasping has been provided in recent experiments conducted by
Bingham (2001) and by Crowell, Todd, and Bingham (2001). A
similar idea has been proposed in connection with 2-D shapes
viewed in a frontoparallel plane (Abrams & Landgraf, 1990;
Gillam, 1998; Gillam & Chambers, 1985; Mack, Heuer, Villardi,
& Chambers, 1985; MacLeod & Willen, 1995; Post & Welch,
1996).
Hypothesis 2: Accurate Perception of Location and
Anisotropy of Perceived Extent
According to this hypothesis, based in part on a model originally
posed by Foley (1991) and subsequently revised by Foley, RibeiroFilho, and Da Silva (2001), a unified visual space exists in which
perceived locations fully constrain the perceived extents. However, the model further predicts that perceived depth extents differ
from perceived width extents; the metric for perceived extent is
computed in terms of the polar coordinates (direction and egocentric distance) of perceived locations and gives greater weight to
directional change than to change in egocentric distance. Hypothesis 2 goes beyond the model of Foley et al. (2001) in assuming
that locations on the ground plane are accurately perceived in both
visual direction and egocentric distance when distance cues are
abundant. As a result, this hypothesis can explain both the accurate
perception of location and the perceptual inequality of depth and
width extents and thus distortion of 2-D shape. Unlike Hypothesis
1, Hypothesis 2 predicts that there cannot be changes in perceived
extent or shape without there being accompanying changes in the
perceived locations defining the extent or shape.
Hypothesis 3: Correction of Misperceived Distance
This hypothesis consists of two assumptions: (a) Perceived
egocentric distance is a compressively nonlinear function of physical distance, and (b) through experience, calibration of the output
transform between perceived distance and the observer’s response
can compensate for the nonlinearity between physical distance and
perceived distance, enabling accurate responding to physical distance. For example, suppose a target 20 m away consistently
appears to be 15 m away. Through experience, an observer could
learn that he or she needs to walk 20 m to arrive at a target that
appears 15 m away. In using this hypothesis to reconcile shape
distortion with accurate egocentric responding, one would further
assume that perceived extents correspond to a metric computed on
the perceived locations in this distorted space. Because a compressive nonlinearity between physical and perceived egocentric distance (e.g., a power function with an exponent of less than one)
would result in greater foreshortening of depth extents than width
extents (for a wide range of metrics), perceived depth extents are
smaller than perceived width extents of equal physical length.
Thus, shape matching and shape judgment tasks ought to reflect
the perceived distortion, because both tasks involve a direct perceptual comparison of the two extents before any output transform
that results in some form of judgment.
Hypothesis 4: Two Visual Systems
According to this hypothesis, visually based action is controlled
by a visuomotor system distinct from that underlying conscious
visual experience, the latter of which is the basis for the visual
matching task. Considerable support for two functionally distinct
visual systems, the parietofrontal system and the occipitotemporal
system, has accrued over the years from research involving both
patients with brain damage (e.g., Marotta, Behrmann, & Goodale,
1997; Milner & Goodale, 1995; Weiskrantz, 1986, 1990) and
neurologically intact observers (e.g., Aglioti, DeSouza, &
Goodale, 1995; Bhalla & Proffitt, 1999; Bridgeman, 1999; Bridge-
DISSOCIATION OF LOCATION AND SHAPE
man, Peery, & Anand, 1997; Creem & Proffitt, 1998; Haffenden &
Goodale, 1998; Proffitt et al., 1995; Servos, 2000; Servos &
Goodale, 1994).
As stated earlier, the four hypotheses are not mutually exclusive.
It is likely that understanding accurate perception of location under
visual conditions in which shape constancy fails will ultimately
require two or more of the hypotheses. In what follows, we note
some of the weaknesses of the various hypotheses.
A weakness of Hypothesis 4 (two visual systems) is that nonmotoric measures of perceived egocentric distance (e.g., verbal
report of distance and measures based on judgments of perceived
size) are often in close agreement with those based on visually
directed action; in particular, reducing the availability of distance
cues has very similar effects on both measures (large scale: Loomis et al., 1998; Loomis & Knapp, in press; Philbeck & Loomis,
1997; small scale: Foley, 1977, 1985). These results indicate that
open-loop visually directed action is controlled by the same internal variable, perceived target location, that underlies the nonmotoric measures. (In contrast, closed-loop visually guided action,
action that is guided by continuously available visual information,
might be controlled in an altogether different way.)
There are at least two weaknesses associated with Hypothesis 3
(correction of misperceived distance). First, few if any observers
ever walk blindly to previewed targets more than 3 m away, so
there should be little opportunity for the hypothesized correction of
the perceptual errors associated with distances beyond 3 m. Second, the first author and his colleagues have conducted a number
of experiments involving variants of visually directed action, the
results of which are inconsistent with the idea of a nonlinearity in
the walking response that compensates for the presumed nonlinearity of visually perceived distance. In triangulation by pointing,
the observer views a target and then walks blindly along an oblique
path while attempting to continue pointing in the direction of the
previously viewed target (Fukusima et al., 1997; Loomis et al.,
1992). In triangulation by walking, the observer views a target and
then walks blindly along an oblique path; at some unexpected
location, the observer is instructed to turn and begin walking
toward the target (Fukusima et al., 1997).
In still another variant, the observer walks blindly along an
oblique path, turns when instructed, and then attempts to walk the
full distance to the target (Loomis et al., 1998; Philbeck et al.,
1997). Loomis et al. (1998) and Philbeck et al. (1997) showed that
when distance cues were abundant, observers walked without
systematic error, whether they walked along a direct or indirect
path; however, when distance cues were sparse, observers made
the expected errors of overwalking to near targets and underwalking to far targets (Philbeck et al., 1997). In both full-cue and
reduced-cue conditions, the mean responses (centroid of stopping
points) for the direct path were very close to those for the indirect
path. This pattern of results refutes the idea of a nonlinearity in the
response process that compensates for the presumed nonlinearity
of visually perceived egocentric distance. Although Hypothesis 3,
as stated, appears untenable, it is possible that a more general
interpretation of Hypothesis 3 is tenable, one that does not involve
calibration through experience but does involve a compensating
nonlinearity in a general response process rather than in one tied to
a specific motor response (e.g., walking along a direct path).
The two remaining hypotheses are not contradicted by existing
evidence, but they do suffer from vagueness about the underlying
1205
computational mechanisms. Still, the two hypotheses separately or
in combination seem promising for explaining the paradoxical
result of accurate perception of location under conditions in which
shape distortion also occurs.
The two experiments reported here lend further support to
Hypothesis 1 in showing that perceived shape can vary even
though the perceived locations of the vertices defining the shape
do not. We report two experiments that complement each other.
The results of Experiment 1 are more robust but were obtained
with methods that leave some ambiguity about interpretation. The
results of Experiment 2 are less striking but more definitive in their
interpretation.
Experiment 1
Method
Observers
A total of 16 observers (10 men and 6 women) from the University of
California at Santa Barbara (UCSB) community were paid for their participation. Their ages ranged from 20 to 29 years (M ⫽ 24 years), and all
were naive about the purposes of the experiment. Their visual acuity was
at least 20/20 (corrected if necessary), as measured by a Keystone (Meadville, PA) orthoscope. All observers were within normal limits of lateral
phoria and had good stereoacuity (25 s of arc or better). The observers were
randomly assigned to participate in either the monocular-viewing group or
the binocular-viewing group, with 8 observers in each group.
Stimuli, Apparatus, and Design
An original aim of this study was to create two viewing configurations
that were nearly projectively equivalent but differed in scale by a ratio of
approximately 8:1. The stimuli were two sets of white spheres 9.8 cm and
1.2 cm in diameter. The precise scale ratio (8.2) we used was determined
by the sizes of these spheres. The large-scale stimuli were seen resting on
the floor of a carpeted indoor laboratory (7.3 m ⫻ 4.3 m). Each observer
viewed these stimuli from an eye height of 150 cm; eye height was
controlled by means of a chin rest. This standing chin rest apparatus,
described elsewhere (Philbeck & Loomis, 1997), could be easily swung out
of the way to permit the observer to walk toward the stimulus after viewing
it. The small-scale stimuli were positioned on a rectangular board (89 cm ⫻
53 cm) painted with a speckled texture that closely resembled the laboratory carpeting. The height of this horizontal surface was adjusted for each
observer to yield an eye height of 18.3 cm when the observer’s head was
held in a nearby chin rest. The viewing distances also varied by the same
8:1 factor across the two scales (large scale: 200, 300, and 400 cm; small
scale: 24.4, 36.6, and 48.8 cm). These distances were measured along the
horizontal viewing surface from a point directly below the observer’s eyes
to the stimulus sphere (or to the nearest sphere in trials presenting several
spheres in combination). The stimuli at the nearest locations of the two
scales were viewed at the same optical slant so that the spheres and their
immediate backgrounds were virtually identical in monocular perspective;
the same was true for the intermediate and farthest distances.
Other than the between-groups monocular– binocular manipulation, all
factors were varied within observers. Each observer performed two perceptual tasks: location judgments (indicating the location of a single sphere
without visual guidance, either by attempting to walk to it [large scale] or
by attempting to place the tip of the index finger there [small scale]) and
extent matches (attempting to adjust the depth extent between two spheres
to match the width extent of two spheres). Extents were specified by a total
of three spheres presented in an L-shaped configuration. The depth extent
was specified by two spheres lying on the ground in the observer’s median
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LOOMIS, PHILBECK, AND ZAHORIK
sagittal plane; the nearest sphere of this pair, together with a third sphere
displaced to the observer’s right in a frontoparallel plane, specified the
width extent. Lateral displacements of the third sphere were 50 cm and 6.1
cm for the large and small scales, respectively.
The scale manipulation was blocked and counterbalanced, with 4 observers in each group seeing the small-scale stimuli first and the others
seeing the large-scale stimuli first. Within each scale block, location
responses were made first, followed by extent matches. On each trial, the
stimuli appeared at one of the three possible distances listed earlier.
On match trials, perceptual matches were created by means of both
ascending and descending series, with two measurements collected apiece.
Three measurements per condition and observer were collected on location
trials. Within blocks, presentation order was completely randomized.
Procedure
The observers wore hearing protectors (noise reduction rating: 25 dB)
to minimize auditory localization information. Monaural sound was
presented through a wireless microphone system (Telex AAR-1 and
TW-6); the observer carried an FM receiver–amplifier and wore small
headphones underneath the hearing protectors, and the experimenter
wore a microphone and transmitter (for more details, see Philbeck et al.,
1997). The observers began each trial with their head immobilized in a
chin rest. For the monocular group, the lateral position of the chin rest
was adjusted so that the observer’s uncovered dominant eye was in the
same sagittal plane as an imaginary line that connected the three
possible egocentric stimulus distances. For the binocular group, the
chin rest was positioned so that the midpoint between the eyes lay in
this plane. The markers used to position the stimuli at both scales were
invisible to the observer. No error feedback was provided in any of the
four trial types described subsequently.
Large-scale, location responses. The observer viewed the single stimulus sphere for approximately 5 s. Afterward, the observer lowered a
blindfold, swung the chin rest to the side, and attempted to walk to the
stimulus location. The stimulus was removed from the observer’s path
before walking began. The experimenter recorded the walked distance as
the straight-line distance from the observer’s starting position to the terminal position. After recording the walked distance, the experimenter
guided the observer (still blindfolded) back to the starting location.
Small-scale, location responses. Observers viewed the stimulus sphere
for approximately 5 s and then closed their eyes and, using their dominant
hand, attempted to place the tip of their index finger at the stimulus
location. The stimulus was removed before observers began to move.
Observers were instructed to first raise their hand above the horizontal
board and then lower their finger to the stimulus location. This instruction
prevented observers from moving their hand along a line of sight until their
index finger met the table, a response that could yield accurate performance
without relying on distance perception.
Extent matches (large and small scales). The observer viewed the
configuration of three spheres. On ascending trials, the far sphere of the
depth pair was initially placed just behind the near sphere; on descending
trials, the far sphere was initially placed approximately 2.5 to 3 times
farther behind the near sphere than the lateral separation between the width
pair of spheres. The observer then directed the experimenter to move the
far sphere closer or farther until the separation between the depth pair
matched the separation between the width pair (objective instructions). To
prevent the observer from being able to scale the distance relations by
relying on motion parallax during the adjustment, we required the observers to close their eyes after each directional instruction (“closer” or “farther”). The experimenter then moved the sphere by a small amount in the
indicated direction while the observer’s eyes were closed.
Results
Figure 2 shows the results of Experiment 1. Because response to
visual direction is usually without systematic error in such a task,
we measured only distance responses. The left-hand panels clearly
show that location responses were unaffected by the monocular–
binocular manipulation, at both the small and large scales. In
striking contrast, the upper right-hand panel shows that this manipulation had a large effect on the small-scale matching of extent.
On average, extent matches made under monocular vision were
nearly 15% larger than those made under binocular vision, even
though judgments of location made under the same viewing conditions showed no hint of this effect. At the larger scale, where the
monocular and binocular views were much more similar, this
effect was attenuated.
To make the indications of distance comparable across scale, we
converted the walking and pointing responses to a signed percentage of the target distance before analysis. An analysis of variance
(ANOVA) confirmed that the distance judgments were not statistically different between the monocular and binocular groups, F(1,
14) ⫽ 0.09, p ⬎ .05; both groups showed a slight underestimation
of about 8% of the target distance. The responses also did not
differ across scale, F(1, 14) ⫽ 1.63, p ⬎ .05, even though different
motor effectors were used to produce the responses, and there was
no Group ⫻ Scale interaction, F(1, 14) ⫽ 0.01, p ⬎ .05. In fact,
none of the main factors and none of their interactions reached
significance.
Each matching response was converted to a ratio between the
depth extent set by the observer and the width extent. A separate
ANOVA performed on these ratios revealed a main effect of the
monocular– binocular manipulation, F(1, 14) ⫽ 6.12, p ⫽ .03, but
this effect was qualified by a significant interaction with scale,
F(1, 14) ⫽ 5.33, p ⫽ .04. Matching ratios were generally smaller
for the binocular group, but this difference was most pronounced
at the small scale. The matching ratios of both groups tended to
increase with the egocentric distance of the stimulus configuration
within each scale, F(2, 28) ⫽ 8.71, p ⬍ .01, but this effect was
significant only at the large scale, F(2, 28) ⫽ 9.08, p ⬍ .01.
Matches made under ascending and descending series did not
differ significantly, F(1, 14) ⫽ 1.66, p ⬎ .05, and there were no
other significant effects.
Immediately after the experimental trials, 2 observers in the
monocular group switched to binocular viewing for a second half
of the experiment, and 2 from the binocular group switched to
monocular viewing. We suspected that any effects of viewing
condition on extent matches would be observable within observers
and wanted to verify this suspicion. However, preliminary data
from these 4 observers showed that there were strong carryover
effects between the viewing condition blocks. After viewing stimuli monocularly, observers continued to exhibit a monocular pattern of responses under binocular viewing (see Figure 2). In a
similar manner, observers who initially viewed stimuli binocularly
continued to produce a binocular pattern of responses under monocular viewing. It is possible that these carryover effects were due
to perseveration in response strategies rather than perseveration in
perceived locations and/or perceived shape. However, rather than
investigating this issue, which was tangential to our primary goal,
we elected to present only the data obtained in the first block for
these 4 observers.
DISSOCIATION OF LOCATION AND SHAPE
1207
Figure 2. Results of Experiment 1. Left: Distance responses for monocular and binocular viewing. The error
bars, when visible, represent ⫾1 SE of the individual observer means. Right: Extent matches for monocular and
binocular viewing. The error bars represent ⫾1 SE of the individual observer means.
Discussion
The major result of this experiment was that, for large and small
scales, the monocular– binocular manipulation had a large effect
on perceived shape, as measured by the extent matching task, but
absolutely no effect on perceived location, as measured by the
walking and pointing tasks. This is consistent with a dissociation
between the perception of shape and the perception of location.2
As mentioned in the introduction, there is accumulating evidence of a dissociation between conscious visual perception and
visually guided action, even among neurologically intact observers. Because the egocentric distance judgments in Experiment 1
were action based and the shape judgments were not, there is the
possibility that the results simply reflect the operation of two
visual pathways, one concerned with conscious visual awareness
and the other with visuomotor control (Hypothesis 4). Indeed,
other research has shown, in the context of reaching and grasping,
that the monocular– binocular manipulation has an influence on
visuomotor responses but no influence on location-based responses associated with conscious perception (Marotta et al., 1997;
Servos, 2000; Servos & Goodale, 1994). In addition, because of
the different types of responses, the results might be interpretable
under Hypothesis 3 (correction of misperceived distance). To
discriminate between Hypothesis 1 and these two alternatives
(Hypotheses 3 and 4), we conducted Experiment 2 using verbal
reports for judgments of both stimulus distance and stimulus
shape.
Experiment 2
Method
Observers
A total of 8 UCSB undergraduates (5 men and 3 women) participated as
observers. Their ages ranged from 16 to 24 years, with a median age of 21
years. Each was paid for participation in the two 1-hr experimental sessions. Visual acuity was verified to be at least 20/30 (corrected if neces-
2
A subsidiary result of Experiment 1 is that the extent matching results
were different at the two scales, for both monocular viewing and binocular
viewing. This contrasts with the results of the study of Loomis and
Philbeck (1999), which showed invariance of shape judgments for monocular viewing and near invariance for binocular judgments. However,
there is no real contradiction between the two studies, because Experiment
2 involved much smaller scale stimuli for which the cues of accommodation, convergence, and binocular disparity would be quite different for the
two scales. The Loomis and Philbeck study (1999) involved nearest egocentric distances of 3.9 and 11.7 m at the small and large scales, respectively.
LOOMIS, PHILBECK, AND ZAHORIK
1208
sary) for all observers. Stereoacuity was also verified to be 25 s of arc or
better for all observers, measured with a Keystone orthoscope.
Stimulus Configuration
Ten L-shaped stimuli were constructed of black-painted cylindrical steel
rods approximately 2 mm in diameter. Sizes and aspect ratios of the stimuli
are shown in Table 1. The stimuli were presented to the observer on a
3-m ⫻ 0.4-m surface with a random textured, light-colored surface shading. The observer’s eye height was set to a fixed position 40.6 cm above the
surface by means of a chin rest apparatus. Eight potential stimulus distances from the observer were chosen, ranging from 0.75 m to 2.5 m in
steps of 0.25 m. It was also possible to rotate the entire experimental
apparatus 180° in the room in which the experiment was conducted. This
rotation afforded changing the viewed background of the room between
experimental sessions.
Design and Procedure
Fifty-four trials were presented to the observer over the course of an
experimental session. Half of the trials were considered dummy trials and
half test trials. We included the dummy trials because we wanted to collect
extensive data on only one aspect ratio but wished the observers to be
exposed to a wider range of aspect ratios. The test trials consisted of the
following stimulus– distance combinations: all L shapes with an aspect
ratio of 2.0 and distances of 1.0, 1.5, and 2.0 m. Each possible stimulus–
distance combination from this subset was presented three times, for a total
of 27 trials. The remaining 27 trials consisted of a random selection of
stimulus– distance combinations. The presentation order of all trials was
randomized, such that the presentation of a dummy or test trial in the case
of any given trial was equally probable. The largest stimulus, a dummy of
aspect ratio 3.0 and base width 20 cm, was never presented from the 2.5-m
distance, however, because at this position the top of the stimulus exceeded
the length of the presentation surface.
Observers made two types of verbally based judgments on every trial: an
aspect ratio judgment (relating to perceived shape) followed by a distance
judgment (relating to perceived location). The aspect ratio judgments were
verbal reports of the depth to width ratio of the L shape, expressed as a
percentage under objective instructions. The distance judgments were
verbal reports of the stimulus distance (i.e., horizontal distance from the
observer to the intersection of the two line segments forming the L figure),
expressed in feet and inches.
Each observer completed two experimental sessions, one performed
under binocular viewing conditions and another performed under monocular conditions. Experimental sessions were conducted on separate days,
with the orientation of the stimulus presentation apparatus rotated 180°
between sessions (to reduce memory carryover). The session order was
determined at random, with half of the observers having received binocular
conditions followed by monocular and half having received monocular
conditions followed by binocular.
Table 1
L-shaped Figure Aspect Ratios Used in Experiment 2, as a
Function of the Base Width of the Stimulus
Aspect ratio
Base width (cm)
1.0
1.5
2.0a
2.5
3.0
10
15
20
No
Yes
No
Yes
Yes
No
Yes
Yes
Yes
No
Yes
No
Yes
Yes
Yes
a
Test value.
Results
The data from 1 observer were excluded from all analyses as a
result of this observer’s expressed confusion about the experimental task. Aspect ratio judgments were normalized by the stimulus
aspect ratio for all subsequent analyses. A four-factor mixeddesign ANOVA was used to analyze this response measure, with
viewing condition order treated as a between-subjects variable and
distance, size, and view conditions treated as within-subject variables. This analysis revealed a significant interaction between
viewing condition and viewing order, F(1, 22) ⫽ 5.86, p ⫽ .02. As
such, a greater difference between monocular and binocular viewing conditions was observed in first-session data than in secondsession data. In light of these carryover effects, we restrict further
discussion to data collected in the first experimental session.
Because this restriction does not allow for within-subject evaluations of the viewing condition variable, a modified analysis was
applied to the data: a three-factor mixed-design ANOVA that
treated distance and size as within-subject variables and viewing
condition as a between-subjects variable. As expected, significant
main effects were observed for both the distance variable, F(2,
44) ⫽ 8.29, p ⬍ .01, and the viewing condition variable, F(1,
22) ⫽ 11.55, p ⬍ .01. Tests of the size variable main effect and all
other interactions proved to be nonsignificant. Figure 3 presents
the first-session shape judgment results collapsed across stimulus
size. The effects of viewing condition are readily apparent. Note
that there is considerable shape distortion in both viewing conditions, as indicated by the normalized aspect ratio values being less
than unity.
The distance data were analyzed in a manner similar to the
shape judgment data. A three-factor mixed-design ANOVA was
conducted on data from the first experimental session only. As
before, this analysis treated distance and size as within-subject
variables and viewing condition as a between-observers variable.
Only the main effect of stimulus distance yielded significant
results, F(2, 44) ⫽ 610.70, p ⬍ .01. A summary of these results is
provided in Figure 4 for the first-session data collapsed across
stimulus size. The most pertinent result was the nonsignificant
difference between the binocular and monocular viewing conditions, F(1, 22) ⬍ 0.01, p ⫽ .97, with both conditions leading to
quite accurate performance.
Discussion
As was the case with the results of Experiment 1, the results here
demonstrate that the monocular– binocular manipulation had a
sizeable effect on the perception of shape, as indicated by the
aspect ratio judgment, but no influence on the judgment of perceived location, as indicated by the distance judgment. Whereas
the results of Experiment 1 might be explained in terms of Hypothesis 3 or 4, the use here of a common response, verbal report,
rules out this possibility. Thus, this experiment provides the strongest evidence of a dissociation between perceived location and
perceived shape in visual space.
General Discussion
The two experiments reported here, along with previous research, show that visually perceived location, as measured by
DISSOCIATION OF LOCATION AND SHAPE
Figure 3. Results of the shape judgment task in Experiment 2: Mean
normalized aspect ratio judgments (first session only) as a function of
target distance and viewing condition. Solid circles represent data from the
binocular condition, and open squares represent data from the monocular
condition. Error bars denote ⫾1 SE of the individual observer means. The
dashed line gives the predicted response for veridical shape perception. The
three dotted lines (corresponding to the three stimulus sizes) give the
predicted responses if perceived shape were equal to retinal shape.
visually directed walking and verbal report, is accurate for binocular and monocular viewing of targets on a horizontal plane. In
contrast, the same research shows that the perception of 2-D
shapes viewed under the same conditions exhibits large systematic
distortion. As discussed in the introduction, four hypotheses have
been proposed as possible ways of reconciling these two findings.
The present research provides support for Hypothesis 1 (accurate
perception of location and dissociation of location and shape). If
perceived shape were linked to the perceived locations of the
vertices defining the shape, any manipulation that changes perceived shape would necessarily involve changes in the perceived
locations of these vertices. Experiments 1 and 2 show that the
distortion observed with monocular viewing decreases significantly with binocular viewing, whereas the monocular– binocular
manipulation has no discernible effect on perceived location. This
is strong evidence for a dissociation within perception. However,
note that the dissociation occurs under special circumstances in
which perspective cues associated with a ground plane provide
reliable information about location. In the absence of such cues,
such as when points of light are viewed without obvious attachment to surfaces, oculomotor cues, binocular cues, and optic flow
must determine perception. Under these conditions, a much tighter
coupling between perceived location and perceived shape or extent
seems to be the case (see Foley, 1980, 1991, in connection with
oculomotor and binocular cues).
Given the large distortions of perceived shape on the surface
plane, it may seem paradoxical that perceived egocentric distance
along the surface plane can be perceived accurately. The fallacy in
thinking that perceived distance must be inaccurate may reside in
the implicit belief that perceived egocentric distance to a target on
1209
the surface plane should be equal to the sum of successive perceived depth extents defined by visually distinct points lying
between the observer and the target. The idea that globally perceived egocentric distance might be the sum of local depth extents
along the ground plane is a special case of the Fechnerian assumption that one can integrate successive just-noticeable differences
along some perceptual dimension to obtain the overall perceptual
difference between the two endpoints. Using just such an assumption, Gilinsky (1951) attempted to derive a scale of perceived
egocentric distance based on a task in which observers constructed
a sequence of equal-appearing physical extents. Given that her
observers adjusted more distant extents as larger so as to appear
equal to nearer extents, the use of the Fechnerian assumption led
to a scale of perceived egocentric distance that was a compressively nonlinear function of physical distance, specifically a hyperbolic function. Because this result is so completely at odds with
the results obtained with visually directed action and other methods (Da Silva, 1985), we conclude that the Fechnerian assumption
is false in this application.
Having supported the hypothesis of a functional dissociation
between perceived location and perceived shape, do we have any
way of explaining it in terms of visual processing? We consider
three mechanistic hypotheses. The first of these hypotheses was
proposed by Walter Gogel (personal communication, April 13,
1996) and is predicated on changes in perception from fixation to
fixation. When we look at a pattern, we successively fixate different parts of the figure. Gogel (1965, 1990) has argued that, for a
given fixation, nonfixated visual targets lying closer or farther than
the fixated target are attracted toward the perceived location of the
latter in accord with the equidistance tendency. The degree of
Figure 4. Results of the distance judgment task in Experiment 2: Mean
verbal reports of distance (first session only) as a function of target
distance. Solid circles represent the data for binocular viewing, and open
squares represent the data for monocular viewing. Error bars denote ⫾1 SE
of the individual observer means. The dashed line represents perfect
responding.
1210
LOOMIS, PHILBECK, AND ZAHORIK
perceptual flattening of the 3-D configuration is the result of a
compromise between the equidistance tendency and the strength of
the relative distance cues; thus, for near stimulus configurations,
strong binocular disparity cues reduce the degree of flattening in
comparison with more distant configurations, for which binocular
disparity is less effective. As applied to the current findings,
Gogel’s hypothesis is that when one fixates a target under full-cue
conditions, the location of the target is perceived correctly, but
nonfixated targets move perceptually toward the fixated target.
Thus, judgments of shapes lying in depth exhibit the distortion
produced by the equidistance tendency, but egocentric responses to
fixated targets are accurate.
Philbeck (2000) has tested and rejected this hypothesis. In his
experiment, observers fixated one of two visible targets lying in
depth on the floor of a well-lit room. Fixation of the target was
controlled by very brief stimulus presentations of the room visible
through a large liquid crystal shutter and by a just-visible fixation
point appearing at the same 3-D location as one of the targets.
After the stimulus configuration and the fixation point had been
blanked, one of the two targets was specified as the destination,
and the observer attempted to walk to its location without vision.
Walked distance, the indicator of perceived distance, showed
accurate responding to all targets, with no tendency whatsoever for
nonfixated targets to move perceptually toward the fixated target.
The second mechanistic hypothesis posits that the perception of
location on the ground plane is based on visual processing that is
quite different from that underlying the perception of shape. We
believe, like many others (e.g., Gibson, 1950a, 1950b; Ooi et al.,
2001; Sedgwick, 1983; Sinai et al., 1998) that perceived egocentric
distance to a target on the surface plane depends strongly on the
perspective cues of texture gradient, linear perspective, and height
in the field (angular elevation and angular declination). Texture
gradient and linear perspective are likely to be the primary bases
for the global organization of the ground plane and its apparent
recession in distance. Any particular point on this perceived
ground plane is specified by its height in the field, so its perceived
egocentric distance is determined by its height in the field acting in
concert with the cues of texture gradient and linear perspective.
Because the perspective cues are sufficient for localizing a point
on the ground plane, binocular information is superfluous. In the
case of shape perception, it is reasonable to suppose that surface
texture is involved in monocularly perceiving the relative sizes of
local extents on the ground plane; if so, the anisotropy of texture
density might explain the distortion of perceived shape, like that
apparent in Figure 1. When viewing switches from monocular to
binocular, the addition of binocular disparity leads to more accurate perception of depth extents and thus reduces the shape
distortion.
The third (and related) hypothesis hinges on the distinction
between central tendency and dispersion. It begins with the assumption that each location in physical space is represented by an
ensemble of graded activity within a population of neurons with
overlapping place fields in three dimensions (analogous to the idea
of receptive fields in two dimensions), with one neuron near the
center of the population typically providing a maximal response.
This profile of graded activity can be characterized by its centroid
and one or more parameters reflecting its dispersion; the dispersion
reflects both the intrinsic connectivity of the visual pathway and
internal noise relating to the quality of the stimulus information
about the target location. According to the second assumption of
this hypothesis, perceived 3-D location corresponds to the centroid
of this profile of graded activity. The degree of dispersion corresponds to the precision with which the location is specified. Thus,
even though two different combinations of distance cues might
determine the same centroid (thus specifying the same location),
they could determine different levels of precision.
The third assumption is that perceived separation between two
targets is analogous to the d⬘ measure of signal detection theory.
Thus, the perceived separation between two physical locations is
equal to the distance between the two centroids, divided by the
dispersion parameter. This hypothesis predicts that distance cues
that increase the precision of the representation (decrease its
spread) will increase the perceived separation between two targets
without modifying the perceived locations of the points. Thus,
adding binocular disparity to monocular perspective cues might
increase the perceived separation between two points in depth
without modifying their perceived locations, as specified by other
cues such as height in the field.
Finally, we note that direct estimates of extent seem to be
subject to less distortion than simultaneous comparison of two
extents. In one of their experiments, Loomis et al. (1992) had
observers walk without vision to two previewed targets on the
ground defining either a width extent or a depth extent. For
equal-sized depth and width extents, observers walked the same
distances. Loomis et al. (1992) speculated that the isotropic walking response could be explained by observers walking in succession to two locations stored in memory. However, Philbeck (1997)
has found that even when observers view two targets and the
extent between them and then estimate the extent using a number
of different responses (e.g., verbal estimate and pacing out a
distance from the viewing position), there is only a slight anisotropy for width and depth extents; a similar result has been reported
by Wender (1999). It appears that when observers abstract the
length of an extent to perform some response other than walking to
its endpoints, their response does not reflect the perceived extent
but is corrected to some degree.
In contrast, when depth and width extents are simultaneously
visible and must be directly compared, either through an extent
matching task (Beusmans, 1998; Loomis et al., 1992) or through a
judgment of aspect ratio, observers do perceive a big difference in
length. This interpretation is supported by an experiment conducted by Amorim, Loomis, and Fukusima (1998), showing that
observers were more accurate in reproducing an L-shaped stimulus
from memory (after viewing it under perspective) than when
reproducing the same shape while viewing it concurrently. In a
similar manner, Vishton, Rea, Cutting, and Nuñez (1999) found
that observers showed a much greater vertical or horizontal illusion when responding simultaneously to the vertical and horizontal
extents of the illusion figure (e.g., when shaping the hand to
respond to both extents) than when responding serially to each
extent. They interpreted their results in terms of a distinction
between the judgment of relative extent (shape) and the judgment
of absolute extent. Without further research, it is unclear whether
this distinction is useful in understanding the present dissociation.
Regardless, the present results indicate that perceived shape does
depend on whether viewing is monocular or binocular, whereas
perceived location does not.
DISSOCIATION OF LOCATION AND SHAPE
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Received September 6, 2000
Revision received October 12, 2001
Accepted February 19, 2002 䡲